Hey! To 'raise a regiment' is to basically arm, equip, clothe, feed etc. a fighting force out of pocket. I'm involved in the Royal Canadian Army Cadets and the 49th Loyal Edmonton Regiment my Corps is affiliated with had been made by a very rich man named Lieutenant Col. Billy Griesbach, they named a base after him but it got renamed I think. Anyway, it's to raise and equip your own force, when the threat of the Central Powers grew extreme, and with the outbreak of WW1, the Dominion of Canada allowed and encouraged the raising of units.

I doubt he would have paid as far as the ship, unless there's some sort of naval/transportation unit attached to the battalion, plus that's the navy's department.

The command structure largely stays the same, except the Lieutenant Colonel/CO/Guy who raised the unit is always kept as a Lieutenant Colonel, typically the highest rank at battalion level.

At that point in history, there was not, as rules I believe were in place against spoils of war, at least somewhat. Plus a letter of marque is typically naval, so I'd have to say no.

Edit: Totally skipped over the questions, sorry.

Do you mean the Lord Strathcona's Horse (LdSH) in particular? If not, can you specify a time period and country/region?